I want each of you to construct a function. Sounds simple enough, right? However, the domain, and
range must both be sets which are not numbers, and each must have at least ten elements. Construct your function
in a logical manner relating the domain to the range.

There are many, many approaches to this problem. The first thing that comes to my mind if we are told to use sets without numbers is to use sets with letters from the alphabet. For instance let S = {A,B,C, ...,X,Y,Z}, the set of all 26 letters. Then we could consider functions from S to S. The easiest function to construct would be the identity function, which we can call id(). Then, id(A) = A, id(B) = B, and so on. A more interesting function would be a function, f, from S to S, which returns the next letter in order, f(A) = B, f(B) = C, and so on. Then, we have to say what f(Z) is (because there is no next letter). With the constraints of the problem we can actually assign f(Z) to any letter we please, but one nice choice would be to set f(Z) = A. For this function, f, and for the identity function, the domain and range are both S, the set of the 26 letters in the alphabet.

Please let me know if you need any clarification. I'm always happy to answer your questions.

This is actually my example, I think I am going to have to have two different sets that are not numbers but relate.

EXAMPLE: For instance, you should write something along the following lines:
Domain = {element 1, element 2,..., element 10}
Range = {element A, element B,..., element J}
f = something which relates elements of Domain to those of Range where
f(element 1) = element C, f(element 2) = element H, etc....

Sep 23rd, 2015

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